A posteriori error analysis for a boundary element method with non-conforming domain decomposition

Catalina Domínguez and Norbert Heuer
Numer. Methods Partial Differential Eq. 30 (3), 947-963, 2014.

We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a non-conforming domain decomposition method based on the Nitsche technique. Assuming a saturation property, we establish quasi-reliability and efficiency of the error estimator in comparison with the error in a natural (non-conforming) norm.
Numerical experiments with uniform and adaptively refined meshes confirm our theoretical results.